Solve for $x$ and $y$ using elimination. $\begin{align*}-8x+y &= 2 \\ 2x-y &= -3\end{align*}$
We can eliminate $y$ when its corresponding coefficients are negative inverses. Add the top and bottom equations. $-6x = -1$ Divide both sides by $-6$ and reduce as necessary. $x = \dfrac{1}{6}$ Substitute $\dfrac{1}{6}$ for $x$ in the top equation. $-8( \dfrac{1}{6})+y = 2$ $-\dfrac{4}{3}+y = 2$ $y = \dfrac{10}{3}$ $y = \dfrac{10}{3}$ The solution is $\enspace x = \dfrac{1}{6}, \enspace y = \dfrac{10}{3}$.